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This paper describes a data-driven framework for approximate globaloptimization in which precomputed solutions to a sample of problems areretrieved and adapted during online use to solve novel problems. This approachhas promise for real-time applications in robotics, since it can producenear-globally optimal solutions orders of magnitude faster than standardmethods. This paper establishes theoretical conditions on how many and wheresamples are needed over the space of problems to achieve a given approximationquality. The framework is applied to solve globally optimal collision-freeinverse kinematics (IK) problems, wherein large solution databases are used toproduce near-optimal solutions in sub-millisecond time on a standard PC.

Learning the Problem-Optimum Map: Analysis and Application to Global Optimization in Robotics